论文标题
Maass Cusp的任意水平和性格的认证
Certification of Maass cusp forms of arbitrary level and character
论文作者
论文摘要
我们提出了一种证明任何级别和特征的任意Maass尖缘形式的方法。这是通过生产正宗的Maass cusp形式的$δ$ eigenValue和声称的$δ$ eigenValue的近似值来实现的。我们将此方法应用于具有二次特征的建议的非CM 5级表格，以介绍该形式的第一个认证的$δ$ - eigenvalue。这项工作概括了Booker，Strömbergsson和Venkatesh提出的认证1级表格的方法，并通过Hejhal和Strömberg开发的方法生产了自称Maass Cusp的任意水平和性格的动机。
We present a method for certifying the existence of an arbitrary Maass cusp form for any level and character. This is accomplished by producing a bound on the difference between the $Δ$-eigenvalue of an authentic Maass cusp form and a purported approximation of a $Δ$-eigenvalue, arrived at by any means. We apply this method to a proposed non-CM level 5 form with quadratic character, to present the first certified $Δ$-eigenvalue of such a form. This work generalises the method for certifying level 1 forms presented by Booker, Strömbergsson and Venkatesh, and is motivated by the production of purported Maass cusp forms of arbitrary level and character via methods developed by Hejhal and Strömberg.
